first-rate vs ace

first-rate is not a noun while ace is a noun.

Word	Noun	Adjective	Verb	Adverb
first-rate	No	Yes	No	Yes
ace	Yes	Yes	Yes	No

As adjectives, first-rate and ace are synonyms defined as:

Other synonyms of first-rate include A-one, crack, super, tiptop, top-notch, topnotch, tops.

first-rate (noun)	ace (noun)
	a serve that the receiver is unable to reach
	one of four playing cards in a deck having a single pip on its face
	someone who is dazzlingly skilled in any field
	the smallest whole number or a numeral representing this number

first-rate (adjective)	ace (adjective)
of the highest quality	of the highest quality

first-rate (adverb)	ace (adverb)
quite well